Free Convection Heat Transfer From a Spherical Shaped Open Cavity

Abstract

A computational work is performed on laminar free convection from an isothermally heated spherical shaped open cavity with negligible wall thickness suspended in the air. Fluid flow and heat transfer are analyzed in detail by solving governing differential equations (continuity, momentum, and energy) numerically over wide ranges of the relevant dimensionless parameters, namely, Rayleigh number, 104 ≤ Ra ≤ 108; and height to diameter ratio, 0.15 ≤ h/D ≤ 0.95. The detailed behavior of thermal and flow fields is delineated by suitable visualization techniques for different Ra and h/D. The influence of Ra and h/D on the local and average Nusselt number is also predicted and it is observed that the average Nusselt number on both outer and inner surfaces decreases with the increase of h/D for a constant value of Ra. A suitable correlation for the net average Nusselt number is obtained for the spherical-shaped open vessel surface as a function of Ra, and h/D based on the computed data points, which is expected to be relevant for various academic and industrial operations. This study can be helpful in various industrial operations, such as heat treatment of foodstuffs, shield surfaces, thermal insulations, melting of polymer pellets, and fluidized reactors.